Scattering intensity, angular dependence

For molecules having dimensions comparable with the wavelength, phase differences will occur between waves scattered from different regions of the molecule. These phase differences result in an angular dependence of the scattered intensity. The reduction may be expressed in temis of a particle interference factor P(2Q) such that... 

Describe the angular dependence of the vertically and horizontally polarized light scattered by a molecule and their resultant by considering the intensity as a vector anchored at the origin whose length in various directions is given by the trigonometric terms in Eqs. (10.25), (10.26), and (10.30),... 

Thus Rg is a constant in any particular experiment where Rayleigh scattering is obtained, since the entire angular dependence of the light intensity is correctly contained in the 1 + cos 6 term. 

The correlator (6) is of the utmost importance because its generating function enters into an expression which describes the angular dependence of intensity of scattering of light or neutrons [3]. It is natural to extend expression (6) for the two-point chemical correlation function by introducing the w-point correlator ya1... (kl...,kn l) which equals the joint probability of finding in a macromolecule n monomeric units Maj.Ma> divided by (n-1) arbitrary sequences... 

Fig. 6. Lower part angular dependence of the non-normalized static scattering intensity I(q) observerd with latex particles (R=265 nm). Upper part dependence of r/q =D on the scattering angle in dynamic LS. The sharp downturn at large scattering angles results from a weak back reflection of light on the boundary of the aqueous solution to the index matching bath, that consisted of toluene. This reflection results from the difference in the refractive indices of water (n = 1.333) and toluene (n =1.51). Reprinted with permission from [182]. Copyright [1982] American Society...

This behavior is not observed uniquely when the angle between the two beams is 90° rather, the intensity of the reflected beam varies continuously with the angle. At 90°, however, the polarization effect is most pronounced. We shall see that some scattering phenomena also show an angular dependence, as well as the fact that scattered light displays maximum polarization at 90°. 

Small-angle X-ray diffraction was performed on three selected fractions (Mw = 13000 45800 91500) within concentrations of 0.5 and 4%. Rigid rodlike geometry of the molecules is indicated in the angular dependence of the scattering intensities. 

The methods of analyzing data for the concentration and angular dependence of the time-average scattering light intensity and the intensity-intensity time correlation function can be found in many LLS books and related literature. In this section, we will mainly concern ourselves with how to combine static and dynamic LLS results to characterize special polymers in regard not only to the average molar mass, but also to the molar mass and composition distributions. 

Figure 4. Open circles, angular dependence of the second-order scattered light intensity (hyper-Rayleigh scattering from 1064 to 532 nm) for a suspension of purple membrane patches of bacteriorhodopsin before any solubilization has taken place. Solid curve best fit to the data by combining the nonlinear hyperpolarizability of retinal with the linear refractive index of the upo-protein.

In static LLS [43], the angular dependence of the excess absolute time-averaged scattering intensity, known as the Rayleigh ratio Rw(< )> is measured. For a dilute solution measured at a relatively small angle (6), Rw(q) can be related to the weight average molar mass (Mw), the root mean square... 

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